What is a thesis?

April 16, 2011

“because i do not hope to turn again
because i do not hope
because i do not hope to turn”
–T. S. Eliot, Ash Wednesday

I have spent the last thirty-six hours, save for time spent sleeping and eating and occasional breaks, working on my senior thesis. Today was particularly frustrating. I began the day with 2500 words and thinking I was almost halfway done. By six in the evening I had 3300 words and still thought I was almost halfway done. I then spent the next nine hours rehashing those 3300 words down to 2300, and now think I’m only a third of the way done.

But, I now have a much clearer conception of what I’m trying to say, so with any luck, the next two-thirds should be easier. Unfortunately, I have my doubts that this is the case, mainly because my argument has three layers, and I have only completed the first; the second and third will likely be just as tricky to figure out. It seems telling that so far, I can only formally summarize part one.

Incidentally, it runs as follows:
People say A and B, but B->A->!B and A->B->!A, so !Au!B
Part two will say something along the lines of,
People say C because A->C and B->C, but !Au!B, but !!C, so must articulate in what sense C.
And part three will articulate in what sense C. But these are too fuzzy at the moment for me to articulate. Again, this is not a good thing.

But the strange thing is, even though I cannot formally articulate my argument–despite the fact that my argument is, at least I think, the kind that can in principle be described formally–I still think I know what my thesis is. And though I find this odd, I’m not sure I can articulate why, which seems fitting.

Incidentally, my thesis is about Cormac McCarthy’s Blood Meridian and the problem of inhuman violence. I’ll probably elaborate once I have it written.

Advertisements

Can Computers Think? Posters

August 31, 2010

I was going to write something up about the question of artificial intelligence and whether or not computers can think. But then I came across this set of posters. So instead of writing anything I’m just going to spend a few hours reading all of them. Sorry.

But you can read them too.


Link: Infinite Life

August 4, 2010

This is a fascinating article about the late 19th century/early 20th century studies in set theory and infinity. I particularly like the accompanying picture. Since I’m not sure the link will work (TNR might be behind a paywall), I’ll reproduce it here:


A Beauty Cold and Austere

August 1, 2010

To keep up the trend of making what are not actual posts, I give you a quotation I recently came across which I think well expresses the idea of what I call “the mathematical sublime.”

Mathematics, rightly viewed, possesses not only truth but supreme beauty — a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, without the gorgeous trapping of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.  The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.
— Bertrand Russell

This isn’t exactly the same as the scientific sublime I used a few weeks ago when discussing Andrew Bird, but it is related. There are two primary differences; first, science, while abstracted from humanity, still deals with the natural world, while mathematics is removed even from that, residing entirely in the realm of logic. This means that while the scientific sublime offers a way of looking at humans as cogs in a machine, the mathematical does not even offer the machine or the cogs — only the rules by which they would, in theory, operate, if they existed.

Second, unlike science, mathematics actually wrestles with infinity. People often go on about “infinity” when they just mean vastness; mathematics actually attempts to quantify the unquantifiable.

Few writers have a true feel for the mathematical sublime, I think (many more can grasp the scientific); the only positive example I can give is Jorge Luis Borges, many of whose stories offer excellent examples of it; see “The Library of Babel.”


Soccer, Baseball, Football

June 16, 2010

The world cup has started. I’ve only seen ten minutes of it; they happened to be the ten minutes in which the US scored its goal against England (or, rather, the English goalie scored against himself). Good luck on my part, I suppose, tuning in when I did.

Unlike the great majority of the world, I’m not a fan of soccer. Partially, I admit, it’s because I’ve never spent the time needed to understand the sport. I have a basic understanding of the rules – even the off-sides rule isn’t that hard to understand, after all (compare it to the arcane definition of a balk) but the strategy of the game I’ve never spent a great deal of effort trying to understand. I don’t have much desire to, though; the game is too fluid for my tastes.

This is really the main distinction between soccer and baseball. When it comes down to it, I suspect, there are really only three kinds of team sports: soccer, which is the same sport as hockey and basketball; baseball, which is the same as cricket; and American football, which is the same as rugby.

  • In soccer (and hockey and basketball), you have a completely fluid game where two sides are trying to get the ball into the opponent’s goal but possession can shift at any time, and there is no clear division of the action except after goals and out-of-bounds, and thus at each division both teams are back to being equal except for the score.
  • In baseball, you have a completely delineated game, where teams take turns going on offense and defense, which involve completely separate goals, and each at-bat is a separate action. The game has basically no fluidity to it, and there are numerous states (having men on base, getting outs) that a play can begin in that make the teams unequal yet with the score remaining the same.
  • In football, you have a strange mix of the two. There are separate offensive and defensive squads, but both teams intend to get the ball in the opponent’s goal, and possession can shift at any time. There are clear divisions between plays, and teams can gain yardage and lose downs without scoring. Yet the basic symmetry of the game gives it a sense of fluidity not found in baseball or soccer.

Of all the professional sports baseball is my favorite, and I think  it is because it is so delineated – it makes it possible to describe it is a step-by-step progression in a way you can’t describe a soccer game. Football I can enjoy for similar reasons, but I find myself easily bored by soccer (though I find it easily the most interesting of the soccer class of games); it always seems the same except when someone scores, and once there’s a score, there’s nothing to be excited about because it’s already back to normal.

Still, I wonder if I wouldn’t like soccer better if it were higher scoring – not as high as basketball games, but more like a baseball game, with an average score being 5-4 not 1-0. That’s about an average football score too, once you factor out the x7 multiplier – a 5-4 game translates into a 35-28 game, which is quite reasonable, and since field goals are only x3 not x7, it makes sense that they tend to be a bit lower than that.

So, though I prefer baseball mainly for its divisions and ability to be analyzed, I wonder if the reason I actively dislike soccer, or at least find it boring, has more to do with the low scores. If a 5-4 score, i.e. 9 total scores, is ideal for a 3-hour-game including commercials (so, a 2-hour game without them), does that mean the proper ratio for sports is a score every 10-15 minutes? Anything significantly more than that leads to a repetitive monotony (in basketball it’s a score every 30 seconds, which is way too often), while anything significantly less leads to a boring game (soccer is probably about a score every 45-60 minutes, though I couldn’t say exactly).

How much deviation from this 10-15 minutes can there be, I wonder, before the sport becomes boring? I also wonder if having such a ratio for some reason requires delineation, separation into different plays. At first glance that may seem preposterous, but it makes a sort of sense. All achievements in sports, I suspect, will be either really difficult (and so happen extremely rarely) or be really easy (and so happen quite often). Delineation means you can have multiple steps that are easy to achieve while requiring that many be achieved in succession in order to score. Having a pitch go in one’s favor is relatively easy; scoring a run requires that happening several times without three outs occurring first. With a more fluid game, you can’t do this, and so either scoring is easy (basketball) and happens too often, or it’s difficult (soccer) and happens too rarely. It’s hard to achieve a good mean.

As a simple thought experiment: consider transforming baseball into a game where there were no gradual accomplishments – it was either all or nothing, every time. The game would consist, basically, of team A making one pitch to team B, and if it results in a home run, team B scores a run; if not, team A comes up to bat. I don’t think that would be a very good game.


Andrew Bird and the Scientific Sublime

June 8, 2010

I haven’t said anything here about music for a while. With this post I intend to rectify that. My subject will be Andrew Bird, an indie-baroque-pop artist, whom I only started listening to in the last few months (probably since January), but who has quickly become one of my favorite musicians. I have three of his albums, “Andrew Bird & The Mysterious Production of Eggs,” “Armchair Apocrypha,” and “Noble Beast”; all three have many good songs on them, some of which I’ll mention over the course of this post.

Andrew Bird has several things going for him. To start with, I find his intricate musical style quite appealing; he plays guitar, violin (pizzicato and arco), and whistles, as well as other instruments, and layers them all together in a way that doesn’t overwhelm –  in fact, his music has a quite minimalistic feel to it, until you pay attention and realize how complex it really is. The whistling in particular makes it unlike most other music I’ve listened to. Andrew Bird songs often give me the feeling of being in a white room looking at a complex yet not chaotic contraption, a clock or perhaps a circuit.

A related strength is his use of his voice and the sound of his lyrics. He doesn’t have an amazingly strong voice, but he uses it to his advantage. It’s melodic yet matter-of-fact, occasionally plaintive, which fits with the precise minimalism of the instrumentals. Then there are the lyrics. The words of his songs always sound as if they mean something, merely by their sound, even if they don’t. For example, he has a song called “Fake Palindromes,” the first few lines of which are, “my dewy-eyed disney bride, what has tried / swapping your blood with formaldehyde?” No one else would try to rhyme with a scientific word like “formaldehyde.”

Which brings me to what I find really interesting about Bird; the subjects of his songs. Given his complex, layered, precise, even scientific, aural aesthetic, it shouldn’t be a surprise that he often takes as his subject science and mathematics. What he is most interested in are the aesthetic and ethical implications of the scientific way of looking at things. He wants to believe in beauty, to have free will, but the fact that we can quantify the universe threatens to make these things impossible. In the song “Masterfade,” he says to his lover that “when you look up at the sky / all you see are zeros / all you see are zeros and ones.” That way of looking at the world, he fears, make a true appreciation of the wonders of the world impossible. In “Imitosis,” he reports (a lot of Andrew Bird songs have the feeling of being reports, perhaps even scientific abstracts) that “What was mistaken for closeness / Was just a case of mitosis.” If we’re just organisms like any other, than whatever meaningful relationships we may have, whatever rights and duties to others we may think we have, are actually just our genetic code controlling us.

But Bird doesn’t go from here to a rejection of science; he loves science and math and logic. You can tell from listening to his songs, to his use of complex latinate words and bizarre conceits and language games. He rejects any attempt, religious or otherwise, to feel better by ignoring what science seems to be saying. In “The Privateers,” he asks of us, “Don’t sell me anything / Your one time offer, so uncalled for / You call it piece of mind.” In “Measuring Cups,” perhaps my favorite Andrew Bird song, he asks, “when you talk about the hand of glory / a tale that’s rather grim and gory / is it just another children’s story that’s been de-clawed? / when the tales of brothers Grimm and Gorey have been outlawed.”

So Bird doesn’t want us to look for meaning by rejecting science. What, then, does he turn to? In the end, I think, he never answers that question in full. If he could, he wouldn’t have to make songs about it. But I think he finds a partial answer in the very scientific aesthetic that resulted from his worrisome interest in science. His songs, after all, though often sounding plaintive and questioning, rarely sound despairing. Instead they revel in their own precision. Rather than seeking beauty outside of science, he finds it in the patterning, of numbers and of sound. This is what the best Andrew Bird songs show us; the precise use of language and sound can conjure images of what they describe that make us feel almost like we’re watching a nature documentary, like with with sea aenenome of “Anonanimal.”

But beauty, I think, might be the wrong word here. He finds aesthetic pleasure in patterns, and beauty is defined as proportion; but more precisely, beauty is found in things being proportionate relative to the viewer. Beauty requires something to be on a human scale. Bird doesn’t find the science beautiful for it’s relationship to humans (in fact, that’s what scares him about it); he finds pleasure in it for its own sake. That sounds to me more like the sublime. And indeed, I think there’s an aspect of reveling in the infinite going on here. Bird is probably one of the few songwriters who would completely understand what it means to say that the world itself is not infinite – it is very large, but bounded. When we draw general laws from it – which is what science does – we are inductively drawing the infinite out of the finite. Bird already intuits this, I think; in “Tenuousness,” he talks about the world, which is “tenuous at best,” coming “just shy of infinity.” The world itself is beyond our grasps and finite; strangely, what is infinite, what is in our minds, is less tenuous.


Poetic Flow Charts

May 2, 2010

For the last month in my Early Modern Literature class we’ve been reading 17th-century poetry. One of my favorite of the poems we’ve read so far has been John Donne’s “Holy Sonnet #5”:

I am a little world made cunningly
Of elements, and an angelic sprite ;
But black sin hath betray’d to endless night
My world’s both parts, and, O, both parts must die.
You which beyond that heaven which was most high
Have found new spheres, and of new land can write,
Pour new seas in mine eyes, that so I might
Drown my world with my weeping earnestly,
Or wash it if it must be drown’d no more.
But O, it must be burnt ; alas ! the fire
Of lust and envy burnt it heretofore,
And made it fouler ; let their flames retire,
And burn me, O Lord, with a fiery zeal
Of Thee and Thy house, which doth in eating heal.

One thing I find really fascinating about this poem is how complex a poetic image is developed over the course of just fourteen lines. Equally fascinating, though, is how diagrammatical it all is; one could, and I have, write up a flow chart showing the movement of imagery in the poem, for it proceeds in an exquisitely logical way. Observe:

(1-2)      |  mind/body (air/earth)
(3-4)      |  -> sin
(4)          |  -> death
(5)          |   ; bible
(6)          |  -> knowledge
(7)          |  -> voyage (water)
(8-9)      |  -> water (drowned/washed)
(10-12)  |  ; fire (sinful)
(12-13)  |  -> fire (purifying)
(14)        |  -> fire (pentecostal; sacramental)

Almost all of the major ideas of the poem are here. Now, the chart is not itself poetic; it’s just a flow chart, after all. But the fact that the chart is possible, and is so interesting in and of itself, is one of the reasons it’s such a great poem. Poems that don’t have this kind of complex thought going on – that just go on  and on about the same thing,  trying to evoke a mood – can be good, but I almost always find much less pleasure in them than intellectually stimulating poems like this.

I suppose that’s probably my mathematical instincts showing through. But come on – even if you like the ambiguity poetry can offer (and I do), don’t you need some structure before there is anything there to be ambiguous with?


%d bloggers like this: